Abstract

The thermal contribution to the nonlinear refractive index of air at 1.064 µm was measured with a high-finesse Fabry–Perot cavity and a 500-mW cw laser beam. At room temperature and pressure, the nonlinear refractive-index coefficient of air was found to be n2th=-1.9±0.2×10-14 cm2/W for a beam waist radius of 0.23 mm and was found to be independent of the relative humidity. The thermal nonlinearities of N2, O2, and CO2 were also measured, and it was found that the dominant contribution to air is its O2 content.

© 2000 Optical Society of America

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  1. G. Martin and R. W. Hellwarth, Appl. Phys. Lett. 34, 371 (1979).
    [CrossRef]
  2. J. O. Tochio, W. Sibbett, and D. J. Bradley, Opt. Commun. 37, 67 (1981).
    [CrossRef]
  3. H. J. Hoffman, J. Opt. Soc. Am. B 3, 253 (1986).
    [CrossRef]
  4. V. I. Bespalov, A. A. Betin, E. A. Zhukov, O. V. Mitropol’sky, and N. Y. Rusov, IEEE J. Quantum Electron. 25, 360 (1989).
    [CrossRef]
  5. D. Jacob, M. Vallet, F. Bretenaker, A. Le Floch, and R. Le Naour, Appl. Phys. Lett. 66, 3546 (1995).
    [CrossRef]
  6. J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, and J. R. Whinnery, J. Appl. Phys. 36, 3 (1965).
    [CrossRef]
  7. A. C. Nilsson, E. K. Gustafson, and R. L. Byer, IEEE J. Quantum Electron. 25, 767 (1989).
    [CrossRef]
  8. R. V. Pound, Rev. Sci. Instrum. 17, 490 (1946).
    [CrossRef] [PubMed]
  9. R. W. P. Drever, J. L. Hall, F. B. Kowalsky, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
    [CrossRef]
  10. D. M. Pennington, M. A. Henesian, and R. W. Hellwarth, Phys. Rev. A 39, 3003 (1989).
    [CrossRef] [PubMed]
  11. R. C. Weast, ed., CRC Handbook of Chemistry and Physics, 68th ed. (CRC, Boca Raton, Fla., 1987).
  12. W. L. Wolfe and G. J. Zissis, eds., The Infrared Handbook (U.S. Office of Naval Research, Arlington, Va., 1978).
  13. We obtained the point at zero humidity by filtering the air through a dry line filter.
  14. J. E. Heebner and R. W. Boyd, Opt. Lett. 24, 847 (1999).
    [CrossRef]
  15. C. O. Weiss, M. Vaupel, K. Staliunas, G. Slekys, and V. B. Taranenko, Appl. Phys. B 68, 151 (1999).
    [CrossRef]

1999

J. E. Heebner and R. W. Boyd, Opt. Lett. 24, 847 (1999).
[CrossRef]

C. O. Weiss, M. Vaupel, K. Staliunas, G. Slekys, and V. B. Taranenko, Appl. Phys. B 68, 151 (1999).
[CrossRef]

1995

D. Jacob, M. Vallet, F. Bretenaker, A. Le Floch, and R. Le Naour, Appl. Phys. Lett. 66, 3546 (1995).
[CrossRef]

1989

A. C. Nilsson, E. K. Gustafson, and R. L. Byer, IEEE J. Quantum Electron. 25, 767 (1989).
[CrossRef]

V. I. Bespalov, A. A. Betin, E. A. Zhukov, O. V. Mitropol’sky, and N. Y. Rusov, IEEE J. Quantum Electron. 25, 360 (1989).
[CrossRef]

D. M. Pennington, M. A. Henesian, and R. W. Hellwarth, Phys. Rev. A 39, 3003 (1989).
[CrossRef] [PubMed]

1986

1983

R. W. P. Drever, J. L. Hall, F. B. Kowalsky, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

1981

J. O. Tochio, W. Sibbett, and D. J. Bradley, Opt. Commun. 37, 67 (1981).
[CrossRef]

1979

G. Martin and R. W. Hellwarth, Appl. Phys. Lett. 34, 371 (1979).
[CrossRef]

1965

J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, and J. R. Whinnery, J. Appl. Phys. 36, 3 (1965).
[CrossRef]

1946

R. V. Pound, Rev. Sci. Instrum. 17, 490 (1946).
[CrossRef] [PubMed]

Bespalov, V. I.

V. I. Bespalov, A. A. Betin, E. A. Zhukov, O. V. Mitropol’sky, and N. Y. Rusov, IEEE J. Quantum Electron. 25, 360 (1989).
[CrossRef]

Betin, A. A.

V. I. Bespalov, A. A. Betin, E. A. Zhukov, O. V. Mitropol’sky, and N. Y. Rusov, IEEE J. Quantum Electron. 25, 360 (1989).
[CrossRef]

Boyd, R. W.

Bradley, D. J.

J. O. Tochio, W. Sibbett, and D. J. Bradley, Opt. Commun. 37, 67 (1981).
[CrossRef]

Bretenaker, F.

D. Jacob, M. Vallet, F. Bretenaker, A. Le Floch, and R. Le Naour, Appl. Phys. Lett. 66, 3546 (1995).
[CrossRef]

Byer, R. L.

A. C. Nilsson, E. K. Gustafson, and R. L. Byer, IEEE J. Quantum Electron. 25, 767 (1989).
[CrossRef]

Drever, R. W. P.

R. W. P. Drever, J. L. Hall, F. B. Kowalsky, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Ford, G. M.

R. W. P. Drever, J. L. Hall, F. B. Kowalsky, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Gordon, J. P.

J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, and J. R. Whinnery, J. Appl. Phys. 36, 3 (1965).
[CrossRef]

Gustafson, E. K.

A. C. Nilsson, E. K. Gustafson, and R. L. Byer, IEEE J. Quantum Electron. 25, 767 (1989).
[CrossRef]

Hall, J. L.

R. W. P. Drever, J. L. Hall, F. B. Kowalsky, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Heebner, J. E.

Hellwarth, R. W.

D. M. Pennington, M. A. Henesian, and R. W. Hellwarth, Phys. Rev. A 39, 3003 (1989).
[CrossRef] [PubMed]

G. Martin and R. W. Hellwarth, Appl. Phys. Lett. 34, 371 (1979).
[CrossRef]

Henesian, M. A.

D. M. Pennington, M. A. Henesian, and R. W. Hellwarth, Phys. Rev. A 39, 3003 (1989).
[CrossRef] [PubMed]

Hoffman, H. J.

Hough, J.

R. W. P. Drever, J. L. Hall, F. B. Kowalsky, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Jacob, D.

D. Jacob, M. Vallet, F. Bretenaker, A. Le Floch, and R. Le Naour, Appl. Phys. Lett. 66, 3546 (1995).
[CrossRef]

Kowalsky, F. B.

R. W. P. Drever, J. L. Hall, F. B. Kowalsky, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Le Floch, A.

D. Jacob, M. Vallet, F. Bretenaker, A. Le Floch, and R. Le Naour, Appl. Phys. Lett. 66, 3546 (1995).
[CrossRef]

Le Naour, R.

D. Jacob, M. Vallet, F. Bretenaker, A. Le Floch, and R. Le Naour, Appl. Phys. Lett. 66, 3546 (1995).
[CrossRef]

Leite, R. C. C.

J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, and J. R. Whinnery, J. Appl. Phys. 36, 3 (1965).
[CrossRef]

Martin, G.

G. Martin and R. W. Hellwarth, Appl. Phys. Lett. 34, 371 (1979).
[CrossRef]

Mitropol’sky, O. V.

V. I. Bespalov, A. A. Betin, E. A. Zhukov, O. V. Mitropol’sky, and N. Y. Rusov, IEEE J. Quantum Electron. 25, 360 (1989).
[CrossRef]

Moore, R. S.

J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, and J. R. Whinnery, J. Appl. Phys. 36, 3 (1965).
[CrossRef]

Munley, A. J.

R. W. P. Drever, J. L. Hall, F. B. Kowalsky, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Nilsson, A. C.

A. C. Nilsson, E. K. Gustafson, and R. L. Byer, IEEE J. Quantum Electron. 25, 767 (1989).
[CrossRef]

Pennington, D. M.

D. M. Pennington, M. A. Henesian, and R. W. Hellwarth, Phys. Rev. A 39, 3003 (1989).
[CrossRef] [PubMed]

Porto, S. P. S.

J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, and J. R. Whinnery, J. Appl. Phys. 36, 3 (1965).
[CrossRef]

Pound, R. V.

R. V. Pound, Rev. Sci. Instrum. 17, 490 (1946).
[CrossRef] [PubMed]

Rusov, N. Y.

V. I. Bespalov, A. A. Betin, E. A. Zhukov, O. V. Mitropol’sky, and N. Y. Rusov, IEEE J. Quantum Electron. 25, 360 (1989).
[CrossRef]

Sibbett, W.

J. O. Tochio, W. Sibbett, and D. J. Bradley, Opt. Commun. 37, 67 (1981).
[CrossRef]

Slekys, G.

C. O. Weiss, M. Vaupel, K. Staliunas, G. Slekys, and V. B. Taranenko, Appl. Phys. B 68, 151 (1999).
[CrossRef]

Staliunas, K.

C. O. Weiss, M. Vaupel, K. Staliunas, G. Slekys, and V. B. Taranenko, Appl. Phys. B 68, 151 (1999).
[CrossRef]

Taranenko, V. B.

C. O. Weiss, M. Vaupel, K. Staliunas, G. Slekys, and V. B. Taranenko, Appl. Phys. B 68, 151 (1999).
[CrossRef]

Tochio, J. O.

J. O. Tochio, W. Sibbett, and D. J. Bradley, Opt. Commun. 37, 67 (1981).
[CrossRef]

Vallet, M.

D. Jacob, M. Vallet, F. Bretenaker, A. Le Floch, and R. Le Naour, Appl. Phys. Lett. 66, 3546 (1995).
[CrossRef]

Vaupel, M.

C. O. Weiss, M. Vaupel, K. Staliunas, G. Slekys, and V. B. Taranenko, Appl. Phys. B 68, 151 (1999).
[CrossRef]

Ward, H.

R. W. P. Drever, J. L. Hall, F. B. Kowalsky, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Weiss, C. O.

C. O. Weiss, M. Vaupel, K. Staliunas, G. Slekys, and V. B. Taranenko, Appl. Phys. B 68, 151 (1999).
[CrossRef]

Whinnery, J. R.

J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, and J. R. Whinnery, J. Appl. Phys. 36, 3 (1965).
[CrossRef]

Zhukov, E. A.

V. I. Bespalov, A. A. Betin, E. A. Zhukov, O. V. Mitropol’sky, and N. Y. Rusov, IEEE J. Quantum Electron. 25, 360 (1989).
[CrossRef]

Appl. Phys. B

R. W. P. Drever, J. L. Hall, F. B. Kowalsky, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

C. O. Weiss, M. Vaupel, K. Staliunas, G. Slekys, and V. B. Taranenko, Appl. Phys. B 68, 151 (1999).
[CrossRef]

Appl. Phys. Lett.

G. Martin and R. W. Hellwarth, Appl. Phys. Lett. 34, 371 (1979).
[CrossRef]

D. Jacob, M. Vallet, F. Bretenaker, A. Le Floch, and R. Le Naour, Appl. Phys. Lett. 66, 3546 (1995).
[CrossRef]

IEEE J. Quantum Electron.

A. C. Nilsson, E. K. Gustafson, and R. L. Byer, IEEE J. Quantum Electron. 25, 767 (1989).
[CrossRef]

V. I. Bespalov, A. A. Betin, E. A. Zhukov, O. V. Mitropol’sky, and N. Y. Rusov, IEEE J. Quantum Electron. 25, 360 (1989).
[CrossRef]

J. Appl. Phys.

J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, and J. R. Whinnery, J. Appl. Phys. 36, 3 (1965).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

J. O. Tochio, W. Sibbett, and D. J. Bradley, Opt. Commun. 37, 67 (1981).
[CrossRef]

Opt. Lett.

Phys. Rev. A

D. M. Pennington, M. A. Henesian, and R. W. Hellwarth, Phys. Rev. A 39, 3003 (1989).
[CrossRef] [PubMed]

Rev. Sci. Instrum.

R. V. Pound, Rev. Sci. Instrum. 17, 490 (1946).
[CrossRef] [PubMed]

Other

R. C. Weast, ed., CRC Handbook of Chemistry and Physics, 68th ed. (CRC, Boca Raton, Fla., 1987).

W. L. Wolfe and G. J. Zissis, eds., The Infrared Handbook (U.S. Office of Naval Research, Arlington, Va., 1978).

We obtained the point at zero humidity by filtering the air through a dry line filter.

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Figures (3)

Fig. 1
Fig. 1

Schematic of the experimental setup. Optical paths are shown as solid lines, and electrical paths are dotted lines. FC, feedback controls; FG, 40-MHz function generator; R, ramp generator driving the piezoelectric transducers; C, computer for data capture. M1, M2, mirrors; L1, L2, lenses; QWP, quarter-wave plate; D2, detector. See text for other definitions.

Fig. 2
Fig. 2

Traces showing the shift of the cavity resonance frequency between (left) low power and (right) high power.

Fig. 3
Fig. 3

Shift of the cavity resonance frequency as a function of the pressure of air within the cavity, for a difference in circulating laser power of 360 W.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

B=FT/π,
Δν=-νΔn/n-νΔn,
Δn=dn/dTΔT,
ΔT=αP/πκlnR/ω0+0.635,
nPN2=-1.9±0.6×10-12 W-1, n2N2=-3.3±1.0×10-15 cm2/W, nPO2=-9.6±0.9×10-11 W-1, n2O2=-1.7±0.2×10-13 cm2/W, nPCO2=-3.8±0.4×10-11 W-1, n2CO2=-6.6±0.7×10-14 cm2/W,
αN2=6.7±2.0×10-10 cm-1, αO2=4.2±0.4×10-8 cm-1, αCO2=5.7±0.6×10-9 cm-1.

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